Presumably to make sure that it's going to the right person!
For any estate, other than a very small one, a bank would normally need to see a grant of probate before releasing the funds. Even for a very small estate though, a bank would at least want to know that they were complying with the terms of the deceased person's will before allowing anyone else to have access to their money. If, say, you could prove that
(a) your parent had died ;
(b) that they weren't married at the time of their death ; and
(c) that you're their only child ;
it still wouldn't mean that you had any right to to their money. (Your parent might, for example, have left everything to Battersea Dogs' Home).